L10-free groups.

If L is a lattice, a group is called L-free if its subgroup lattice has no sublattice isomorphic to L. It is easy to see that L10, the subgroup lattice of the dihedral group of order 8, is the largest lattice L such that every finite L-free p-group is modular. Therefore in this paper we study finite L10-free groups and show that such a group is soluble and (with rather few exceptions) has metacyclic Fitting factor group. [ABSTRACT FROM AUTHOR]